2500 VIBRATIONS

2001 Dodge Ram

I have a 2001 Dodge Ram 2500 that has a vibration noise at 50 to 70 mph. The vibrations only start when I release the gas pedal and stops when I put my foot back on the gas pedal. It sounds loud and coming from the firewall / floor board area. It vibrates all the way to my dash. Other problems is that when the trans is cold my truck goes into reverse kind of ruff. Also I have a tail pipe that is loose. Any ideas?